Question: A circle with circumference $10\pi$ has an arc with a $\dfrac{4}{3}\pi$ radians central angle. What is the length of the arc? ${10\pi}$ ${\dfrac{4}{3}\pi}$ $\color{#DF0030}{\dfrac{20}{3}\pi}$
Answer: The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{4}{3}\pi \div 2 \pi = \dfrac{s}{10\pi}$ $\dfrac{2}{3} = \dfrac{s}{10\pi}$ $\dfrac{2}{3} \times 10\pi = s$ $\dfrac{20}{3}\pi = s$